Consistency reasoning in lattice-based fuzzy Description Logics
Consistency reasoning in lattice-based fuzzy Description Logics
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DOI：
10.1016/j.ijar.2013.07.006
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
Stefan Borgwardt;R. Peñaloza
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文献类型：
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作者：
Stefan Borgwardt;R. Peñaloza
摘要模糊描述逻辑作为一种模糊知识表示和推理的形式化方法已得到广泛的研究。在（模糊）描述逻辑中，最基本的推理任务之一是判断表示知识域的本体是否一致。令人惊讶的是，不太了解这个问题的复杂性语义的基础上完成德摩根格。为了弥补这一空白，在本文中，我们详细研究了模糊描述逻辑L-SHI及其子逻辑的一致性问题。该文件的贡献是双重的。一方面，我们提供了一个基于表格的算法来决定一致性时，底层格是有限的。该算法概括了经典SHI开发的一个。另一方面，我们确定了无限格上的模糊描述逻辑的可判定类和不可判定类。对于所有的可判定类，我们也提供了严格的复杂性界限。
Abstract Fuzzy Description Logics have been widely studied as a formalism for representing and reasoning with vague knowledge. One of the most basic reasoning tasks in (fuzzy) Description Logics is to decide whether an ontology representing a knowledge domain is consistent. Surprisingly, not much is known about the complexity of this problem for semantics based on complete De Morgan lattices. To cover this gap, in this paper we study the consistency problem for the fuzzy Description Logic L-SHI and its sublogics in detail. The contribution of the paper is twofold. On the one hand, we provide a tableaux-based algorithm for deciding consistency when the underlying lattice is finite. The algorithm generalizes the one developed for classical SHI. On the other hand, we identify decidable and undecidable classes of fuzzy Description Logics over infinite lattices. For all the decidable classes, we also provide tight complexity bounds.